Fractal
Videos
In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals
Highly magnified area on the boundary of the Mandelbrot set
The Mandelbrot set: its boundary is a fractal curve with Hausdorff dimension 2. (Note that the colored sections of the image are not actually part of the Mandelbrot Set, but rather they are based on how quickly the function that produces it diverges.)
Mandelbrot set with 12 encirclements
2x 120 degrees recursive IFS
Mandelbrot set
Videos
The Mandelbrot set is a two-dimensional set. It is defined in the complex plane as the complex numbers c for which the function f c = z 2 + c does not diverge to infinity when iterated starting at z =
Fractal
…dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry…
Gap between the "head" and the "body", also called the "seahorse valley"
Double-spirals on the left, "seahorses" on the right